International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 8, Pages 569-572
doi:10.1155/S016117120000048X
How to generate all integral triangles containing a given angle
Department of Mathematics, Bowie State University, Bowie 20715, MD, USA
Received 24 April 1998
Copyright © 2000 Nelson Petulante and Ifeoma Kaja. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We present an elementary prescription based on the
rational secant method for generating all the integral triangles containing a given angle of rational cosine. This is a direct generalization
of the ancient problem of finding all the Pythagorean triples. As
an example, we discuss a specific equation studied by Diophantus of
Alexandria, which turns out to be equivalent to the problem of
finding all the integral triangles containing a
60∘ angle. The material developed here is elementary
enough for inclusion in undergraduate courses and advanced high
school courses.